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Chemistry LibreTexts

10.E: Nuclear and Chemical Reactions (Exercises)

  • Page ID
    59419
  • These are homework exercises to accompany Chapter 10 of the University of Kentucky's LibreText for CHE 103 - Chemistry for Allied Health. Answers are below the questions.

    Questions

    (click here for solutions)

    Q10.1.1

    Write the symbol for the isotope described.

    1. 12 protons, 12 electrons, 13 neutrons
    2. 17 protons, 17 electrons, 20 neutrons
    3. 53 protons, 53 electrons, 78 neutrons
    4. 92 protons, 92 electrons, 146 neutrons

    Q10.1.2

    Determine the number of protons, neutrons, and electrons in each isotope.

    1. \(\ce{^{195}_{77}Ir}\)
    2. \(\ce{^{209}_{82}Pb}\)
    3. \(\ce{^{211}_{84}Po}\)
    4. \(\ce{^{237}_{93}Np}\)

    Q10.1.3

    Fill in the missing numbers in each equation.

    1. \(\ce{^{196}_{82}Pb}\) + \(\ce{^0_{-1}e}\) → \(_{\text{__}}^{\text{__}}\text{Tl}\)
    2. \(\ce{^{28}_{15}P}\) → \(_{\text{__}}^{\text{__}}\text{Si}\) + \(\ce{^0_1e}\)
    3. \(\ce{^{226}_{88}Ra}\) → \(_{\text{__}}^{\text{__}}\text{Rn}\) + \(\ce{^4_2 \alpha}\)
    4. \(\ce{^{73}_{30}Zn}\) → \(_{\text{__}}^{\text{__}}\text{Ga}\) + \(\ce{^0_{-1}e}\)

    Q10.1.4

    Fill in the blanks for each of the nuclear reactions below. State the type of decay in each case.

    1. \(\ce{^{198}_{79}Au}\) → _______ + \(\ce{^0_{-1}e}\)
    2. \(ce{^{57}_{27}Co}\) + \(\ce{^0_{-1}e}\) → _______
    3. \(\ce{^{230}_{92}U}\) → _______ + \(\ce{^4_2He}\)
    4. \(\ce{^{128}_{56}Ba}\) → _______ + \(\ce{^0_{1}e}\)
    5. \(\ce{^{131}_{53}I}\) → \(\ce{^{131}_{54}Xe}\) + _______
    6. \(\ce{^{239}_{94}Pu}\) → \(\ce{^{235}_{92}U}\) + _______

    Q10.1.5

    Write balanced nuclear reactions for each of the following.

    1. Francium-220 undergoes alpha decay.
    2. Arsenic-76 undergoes beta decay.
    3. Uranium-231 captures an electron.
    4. Promethium-143 emits a positron.

    (click here for solutions)

    Q10.2.1

    Describe the main difference between fission and fusion.

    Q10.2.2

    What is the difference between the fission reactions used in nuclear power plants and nuclear weapons?

    Q10.2.3

    How do the doses of radioisotopes used in diagnostic procedures and therapeutic treatment compare to one another?

    (click here for solutions)

    Q10.3.1

    What percent of a sample remains after one half-life? Three half-lives?

    Q10.3.2

    The half-life of polonium-218 is 3.0 min. How much of a 0.540 mg sample would remain after 9.0 minutes have passed?

    Q10.3.3

    The half-life of hydrogen-3, commonly known as tritium, is 12.26 years. If 4.48 mg of tritium has decayed to 0.280 mg, how much time has passed?

    Q10.3.4

    The half-life of protactinium-234 is 6.69 hours. If a 0.812 mg sample of Pa-239 decays for 40.14 hours, what mass of the isotope remains?

    Q10.3.5

    2.86 g of a certain radioisotope decays to 0.358 g over a period of 22.8 minutes. What is the half-life of the radioisotope?

    Q10.3.6

    Use Table 10.3.2 above to determine the time it takes for 100. mg of carbon-14 to decay to 6.25 mg.

    Q10.3.7

    A radioisotope decays from 55.9 g to 6.99 g over a period of 72.5 hours. What is the half-life of the isotope?

    Q10.3.8

    A sample of a radioisotope with a half-life of 9.0 hours has an activity of 25.4 mCi after 36 hours. What was the original activity of the sample?

    Q10.3.9

    What volume of a radioisotope should be given if a patient needs 125 mCi of a solution which contains 45 mCi in 5.0 mL?

    Q10.3.10

    Sodium-24 is used to treat leukemia. A 36-kg patient is prescribed 145 μCi/kg and it is supplied to the hospital in a vial containing 250 μCi/mL. What volume should be given to the patient?

    Q10.3.11

    Using information from the previous question and knowing the half-life of Na-24 is 15 hours, calculate the total dose in μCi given to the patient. How long will it take for the radioactivity to be approximately 80 μCi?

    Q10.3.12

    Lead-212 is one of the radioisotopes used in the treatment of breast cancer. A patient needs a 15 μCi dose and it is supplied as a solution with a concentration of 2.5 μCi/mL. What volume does the patient need? Given the half-life of lead is 10.6 hours, what will be the radioactivity of the sample after approximately four days?

    (click here for solutions)

    Q10.4.1

    Identify each of the following as a physical or chemical change.

    1. melting ice
    2. boiling water
    3. cooking eggs
    4. dissolving salt in water
    5. burning match
    6. metal reacting with HCl
    7. mixing NaCl and KCl
    8. decomposition of hydrogen peroxide

    Q10.4.2

    Give two signs that indicate a chemical change is occurring.

    Q10.4.3

    What doesn't change when a substance undergoes a physical change?

    (click here for solutions)

    Q10.5.1

    Identify the reactants and products in each chemical reaction.

    1. In photosynthesis, carbon dioxide and water react to form glucose and oxygen.
    2. Magnesium oxide forms when magnesium is exposed to oxygen gas.

    Q10.5.2

    Write grammatically correct sentences that completely describe the chemical reactions shown in each equation. You may need to look up the names of elements or compounds.

    1. 2H2O2(l) → 2H2O(l) + O2(g)
    2. CuCO3(s) → CuO(s) + CO2(g)
    3. 2Cs(s) + 2H2O(l) → 2CsOH(aq) + H2(g)

    Q10.5.3

    How many atoms of each element are represented by the following combinations of coefficients and chemical formulas?

    1. 5Br2
    2. 2NH3
    3. 4(NH4)2SO4
    4. 2CH3COOH
    5. 3Fe(NO3)3
    6. 2K3PO4

    Q10.5.4

    Balance the following equations.

    1. Zn(s) + HCl(aq) → ZnCl2(aq) + H2(g)
    2. Li(s) + N2(g) → Li3N(s)
    3. Ca(OH)2 + HBr → CaBr2 + H2O
    4. C4H10 + O2 → CO2 + H2O
    5. NH3 + CuO → Cu + N2 + H2O

    Q10.5.5

    Balance the following equations.

    1. Fe(s) + Cl2(g) → FeCl3(g)
    2. C4H10O + O2 → CO2 + H2O
    3. As + NaOH → Na3AsO3 + H2
    4. SiO2 + HF → SiF4 + H2O
    5. N2 + O2 + H2O → HNO3

    Answers

    10.1: Nuclear Radiation

    Q10.1.1

    Write the symbol for the isotope described.

    1. \(_{12}^{25}\text{Mg}\)
    2. \(_{17}^{37}\text{Cl}\)
    3. \(_{53}^{131}\text{I}\)
    4. \(_{92}^{238}\text{U}\)

    Q10.1.2

    1. 77 protons, 77 electrons, 118 neutrons
    2. 82 protons, 82 electrons, 127 neutrons
    3. 84 protons, 84 electrons, 127 neutrons
    4. 93 protons, 93 electrons, 144 neutrons

    Q10.1.3

    1. \(\ce{^{196}_{82}Pb}\) + \(\ce{^0_{-1}e}\) →\(_{81}^{196}\text{Tl}\)
    2. \(\ce{^{28}_{15}P}\) → \(_{14}^{28}\text{Si}\) + \(\ce{^0_1e}\)
    3. \(\ce{^{226}_{88}Ra}\) → \(_{86}^{222}\text{Rn}\) + \(\ce{^4_2 \alpha}\)
    4. \(\ce{^{73}_{30}Zn}\) → \(_{31}^{73}\text{Ga}\) + \(\ce{^0_{-1}e}\)

    Q10.1.4

    1. \(\ce{^{198}_{79}Au}\) → \(_{80}^{198}\text{Hg}\) + \(\ce{^0_{-1}e}\), beta
    2. \(\ce{^{57}_{27}Co}\) + \(\ce{^0_{-1}e}\) → \(_{26}^{57}\text{Fe}\), electron capture
    3. \(\ce{^{230}_{92}U}\) → \(_{90}^{226}\text{Th}\) + \(\ce{^4_2He}\), alpha
    4. \(\ce{^{128}_{56}Ba}\) → \(_{55}^{128}\text{Cs}\) + \(\ce{^0_{1}e}\), positron
    5. \(\ce{^{131}_{53}I}\) → \(\ce{^{131}_{54}Xe}\) + \(_{-1}^{0}e\), beta
    6. \(\ce{^{239}_{94}Pu}\) → \(\ce{^{235}_{92}U}\) + \(_{2}^{4}\alpha\) (or can show as \(_{2}^{4}\text{He}\)), alpha

    Q10.1.5

    1. \(_{87}^{220}\text{Fr}\;\rightarrow\;_{2}^{4}\text{He}\;+\;_{85}^{216}\text{At}\)
    2. \(_{33}^{76}\text{As}\;\rightarrow\;_{-1}^{0}e\;+\;_{34}^{76}\text{Se}\)
    3. \(_{92}^{231}\text{U}\;+\;_{-1}^{0}e\;\rightarrow\;_{91}^{231}\text{Pa}\)
    4. \(_{61}^{143}\text{Pm}\;\rightarrow\;_{1}^{0}e\;+\;_{60}^{143}\text{Nd}\)

    10.2: Fission and Fusion

    Q10.2.1

    During fission, big nuclei split into smaller nuclei. During fusion, nuclei combine to form large nuclei.

    Q10.2.2

    Fission in nuclear power plants is controlled through limiting the availability of neutrons. Nuclear weapons are uncontrolled once the process initiates.

    Q10.2.3

    Diagnostic amounts are much smaller than therapeutic amounts.

    10.3: Half-Life

    Q10.3.1

    1 half-life: 50%

    3 half-lives: 12.5%

    Q10.3.2

    Time Half-lives Amount
    0 minutes 0.540 mg
    3 minutes 1 0.270 mg
    6 minutes 2 0.135 mg
    9 minutes 3 0.0675 mg

    Q10.3.3

    Amount Half-lives Time
    4.48 mg 0 years
    2.24 mg 1 12.26 years
    1.12 mg 2 24.52 years
    0.560 mg 3 36.78 years
    0.280 mg 4 49.04 years

    Q10.3.4

    Time Half-lives Amount
    0 hours 0.812 mg
    6.69 hours 1 0.406 mg
    13.38 hours 2 0.203 mg
    20.07 hours 3 0.102 mg
    26.76 hours 4 0.0508 mg
    33.45 hours 5 0.0254 mg
    40.14 hours 6 0.0127 mg

    Q10.3.5

    Amount Half-lives
    2.86 g
    1.43 g 1
    0.715 g 2
    0.358 g 3

    It takes three half-lives to go from 2.86 g to 0.358 g in a total time of 22.8 minutes.

    \(22.8\;min\;\div\;3\;=7.60 \;min\)

    One half-life is 7.60 minutes.

    Q10.3.6

    Amount Half-lives Time
    100. mg 0 years
    50.0 mg 1 5730 years
    25.0 mg 2 11460 years
    12.5 mg 3 17190 years
    6.25 mg 4 22920 years

    Q10.3.7

    Amount Half-lives
    55.9 g
    28.0 g 1
    14.0 g 2
    6.99 g 3

    It takes three half-lives to go from 55.9 g to 6.99 g in a total time of 72.5 hours.

    \(72.5\;hr\;\div\;3\;=24.2 \;hr\)

    One half-life is 24.2 hours.

    Q10.3.8

    Fill in the time and half-lives from top to bottom. Start at the bottom of the amount column to fill it in because we know where we end up but not where we started.

    Time Half-lives Activity
    0 hours 406 mCi
    9.0 hours 1 203 mCi
    18 hours 2 102 mCi
    27 hours 3 50.8 mCi
    36 hours 4 25.4 mCi \(\leftarrow\) START HERE

    Q10.3.9

    \(125\;mCi\left(\frac{5.0\;mL}{45\;mCi}\right)=14\;mL\)

    Q10.3.10

    Sodium-24 is used to treat leukemia. A 36-kg patient is prescribed 145 μCi/kg and it is supplied to the hospital in a vial containing 250 μCi/mL. What volume should be given to the patient?

    \(36\;kg\left(\frac{145\;\mu Ci}{kg}\right)\left(\frac{1\;mL}{250\;\mu Ci}\right)=21\;mL\)

    Q10.3.11

    \(21\;mL\left(\frac{250\;\mu Ci}{mL}\right)=5250\;\mu Ci\) is the total dose received

    Amount Half-lives Time
    5250 μCi 0 hours
    2625 μCi 1 15 hours
    1313 μCi 2 30 hours
    656 μCi 3 45 hours
    328 μCi 4 60 hours
    164 μCi 5 75 hours
    82 μCi 6 90 hours

    Q10.3.12

    Lead-212 is one of the radioisotopes used in the treatment of breast cancer. A patient needs a 15 μCi dose and it is supplied as a solution with a concentration of 2.5 μCi/mL. What volume does the patient need? Given the half-life of lead is 10.6 hours, what will be the radioactivity of the sample after approximately four days?

    Volume given: \(15\;\mu Ci\left(\frac{1\;mL}{2.5\;\mu Ci}\right)=6.0\;mL\)

    Elapsed time in hours: \(4\;days\left(\frac{24\;hr}{day}\right)=96\;hr\)

    Time Half-lives Activity
    0 hours 15 μCi
    10.6 hours 1 7.5 μCi
    21.2 hours 2 3.8 μCi
    31.8 hours 3 1.9 μCi
    42.4 hours 4 0.94 μCi
    53.0 hours 5 0.47 μCi
    63.6. hours 6 0.23 μCi
    74.2 hours 7 0.12 μCi
    84.8 hours 8 0.059 μCi
    95.6 hours 9 0.029 μCi

    10.4: Physical and Chemical Changes

    Q10.4.1

    1. physical
    2. physical
    3. chemical
    4. physical
    5. chemical
    6. chemical
    7. physical
    8. chemical

    Q10.4.2

    Any two from change in color, formation of gas (i.e. bubbles), formation of precipitate, odor, change in temperature.

    Q10.4.3

    chemical composition (i.e. chemical formula is the same)

    10.5: Chemical Equations

    Q10.5.1

    1. reactants: carbon dioxide and water; products: glucose and oxygen
    2. reactants: magnesium and oxygen; product: magnesium oxide

    Q10.5.2

    Descriptions may vary.

    1. Two moles of liquid hydrogen peroxide decomposes to form two moles of liquid water and one mole of gaseous hydrogen.
    2. One mole of solid copper(II) carbonate decomposes to form one mole each of solid copper(II) oxide and gaseous carbon dioxide.
    3. Two moles of solid cesium react with 2 moles of liquid water to form 2 moles of aqueous cesium hydroxide and 1 mole of gaseous hydrogen.

    Q10.5.3

    1. 10 Br
    2. 2 N, 6 H
    3. 8 N, 32 H, 4 S, 16 O
    4. 4 C, 8 H, 4 O
    5. 3 Fe, 9 N, 27 O
    6. 6 K, 2 P, 8 O

    Q10.5.4

    1. Zn(s) + 2 HCl(aq) → ZnCl2(aq) + H2(g)
    2. 6 Li(s) + N2(g) → 2 Li3N(s)
    3. Ca(OH)2 + 2 HBr → CaBr2 + 2 H2O
    4. 2 C4H10 + 13 O28 CO2 + 10 H2O
    5. 2 NH3 + 3 CuO → 3 Cu + N2 + 3 H2O

    Q10.5.5

    1. 2 Fe(s) + 3 Cl2(g) → 2 FeCl3(g)
    2. C4H10O + 6 O24 CO2 + 5 H2O
    3. 2 As + 6 NaOH → 2 Na3AsO3 + 3 H2
    4. SiO2 + 4 HF → SiF4 + 2 H2O
    5. 2 N2 + 5 O2 + 2 H2O → 4 HNO3
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